New aspects of second-harmonic optical activity from chiral surfaces and interfaces

New expressions are developed within the electric dipole approximation for the four Stokes parameters characterizing the polarization properties of coherent second-harmonic radiation generated from chiral isotropic surfaces in reflection. These are employed to derive, in addition to the three well-known incident circular polarization second-harmonic optical activity (SHOA) observables, thirteen new basic observables for the detection of surface SHOA which involve second-harmonic intensity difference measurements using right and left circular, and +45 degrees and -45 degrees linear, polarization modulation in the incident and second-harmonic radiation and in both simultaneously. Because of their dependence on a fully electric dipole allowed tensor these circular and linear intensity differences and the corresponding intensity sums have the same order of magnitude, so that all the dimensionless surface SHOA effects they generate are of the order of unity. The circular intensity differences (CIDs) depend on the imaginary part of products of second-order surface susceptibility tensor components and can therefore be observed only under preresonance or resonance scattering conditions; whereas the linear intensity differences (LIDs) depend on the real part of the same tensor component products and can therefore also be detected at transparent frequencies. Employing elliptically polarized incident radiation, appropriate combinations of CIDs and LIDs also measure, respectively, real and imaginary parts of the relevant surface susceptibility tensor products so that a suitable CID combination may also be detected under non-resonance scattering conditions. The best experimental strategies are identified for SHOA detection and extraction of complete SHOA information and relationships are discussed between the SHOA observables and the second-harmonic polarization azimuth, ellipticity and degree of polarization. Because only pure electric dipole scattering processes are considered, the basic formalism applies also to magnetically induced SHOA phenomena.